Mr. Paul, who has previously called for Mr. Geithner to resign, took to the Senate floor Wednesday and complained that the U.S. has spent three years under financial policy “that is not working.” He said that “we got here through bad economic policy” that “originated with Timothy Geithner, when he was at the Federal Reserve of New York.

“I would respectfully ask at this point that we have a vote,” Mr. Paul said. “I think the American people have already given a vote of no confidence in the secretary of Treasury.”

Mr. Paul’s request appears more symbolic than substantive since the Democratic-controlled Senate is unlikely to schedule such a vote.

A Treasury spokeswoman was not immediately available to comment.

Mr. Geithner, who had reportedly been considering stepping down as Treasury secretary after Congress reached a deal to raise the U.S. borrowing limit, last month told U.S. President Barack Obama he planned to stay in the position.